Facilitating data transfer and improving precision in capillary zone

Real-Time Measurement of Electroosmotic Flow in Capillary Zone Electrophoresis. Thomas T. Lee , Rajeev. Dadoo , and Richard N. Zare. Analytical Chemis...
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Anal. Chem. 7991, 63,2842-2848

Facilitating Data Transfer and Improving Precision in Capillary Zone Electrophoresis with Migration Indices Thomas T. Lee and Edward S. Yeung* Department of Chemistry and Ames Laboratory- USDOE, Iowa State University, Ames, Iowa 50011

A m@atkn index and an adJusted migration hdex for capillary zone eiectrophoresk (CZE) are introduced. Use of the Indices makes possible the transfer of migration data obtained with different constant or gradient potentials. Results from capillaries with distinct lengths, inner diameters, and { potentials can a b be related. Furhemme, improvement in the precision of migration data is reailzed. The performances of the mlgratlon Indices, mlgratlon time, reiatlve migratlon and electrophoretic mobility are compared In typlcai analytical runs, and the relative merits and drawbacks of each Indicator are discussed.

INTRODUCTION The tremendous potential that capillary zone electrophoresis (CZE) holds in modem separation science is well-known (1-3). The unparalleled efficiency and speed of CZE in the resolution of involatile and thermally labile species have led to its ever increasing popularity. This is reflected in the availability of commercial instruments from several companies on the market. With the rapid development in the field of biotechnology, it is certain that CZE will play an even larger role in the analytical arena in the future. Much like gas chromatography (GC) in the 1960s and high-performance liquid chromatography (HPLC) in the 1970s, the current version of CZE is plagued with several problems which preclude its routine and wide-spread use. Most notably, problems associated with poor migration time and quantitative precision, anaiytewall interaction, unreliable coating manufacturing procedures, inaccurate temperature control and low detector sensitivity remain to be solved. While many fine efforts have been expended in the areas of the coating and detection technologies, the aspects of migration time precision and reproducibility have received relatively little attention. In fact, as the application of CZE expands in scope and complexity, more stringent requirements will likely be placed upon the accuracy and precision with which analytes can be specified in an electropherogram. The reliable transfer of results between laboratories is vital for quality control/quality assurance purposes, whether for satisfying government protocols or ensuring product quality. Furthermore, the ability to relate resulta obtained under different separation conditions would prove to save both time and effort in method development. In this context, research directed toward addressing these issues is paramount to the general acceptance of CZE as a mainstream analytical technique. In the present work, the mechanisms and problems underlying the behavior of migration times are discussed. Two migration indices are then introduced to circumvent some of these shortcomings. Finally, experiments are carried out to compare the performances of these parameters in typical analytical runs. THEORY Problems with Electrophoretic Mobility and Migration Time. Separation in CZE is achieved via the distinct 0003-2700/91/0383-2842$02.50/0

migration velocities of analytes under the influence of an electric field. An analyte is typically identified by ita migration time (t,) in an electropherogram. A more general parameter that specifies an analyte is the electrophoretic mobility (pep). When contributions from the relaxation effect are neglected, pepcan be expressed as ( 4 )

where t is the dielectric constant of the medium, lathe { potential of the analyte, q the viscosity coefficient, K the reciprocal of the analyte double layer thickness, a the "radius" of the analyte and f(Ka) is a function dependent upon the shape and Ka of the analyte in the buffer. The electrophoretic migration velocity (ueP) of an analyte is as follows:

where E ( = V / L ) is the local electric field, V the applied potential, and L the length of the capillary. The approximation is valid if E is constant throughout the capillary. This will be the case when the analyte is present at much lower concentrations compared to the buffer components. We will also neglect band distortions due to differences in electrophoretic mobility between the analyte and the buffer ions, which will affect out ability to determine v. In all practical situations, the velocity of electroosmotic flow (v,) in a cylindrical capillary is given by (5) veo =

Elcs -

tl

(3)

where lcis the l potential of the inner wall of the capillary and the proportionality constant relating u, to E is known as the electroosmotic flow coefficient (p,). Strictly speaking, the 7's in eqs 1 and 3 are different (analyte-solution vs wall-solution). For most applications however, they can be treated as being identical. Combination of eqs 1, 2, and 3 yields the following expression for v, the net migration velocity of an analyte: (4)

It follows that the analyte migration time is

As shown in eq 5 , t , is dependent upon E , L, l,,and l,f(Ka). While E and L can freely be chosen by the practitioner, lcand laf(Ka)are essentially determined by the nature of the running buffer, i.e. pH, electrolyte type, electrolyte concentration, solvent and, in the case of laf',f(Ka), the analyte itself. Although it is possible to control Cc (without affecting {,f(Ka)) by means of an external electric field (6) or addition of a surfactant to 0 199 1 American Chemical Society

ANALYTICAL CHEMISTRY, VOL. 63, NO. 24, DECEMBER 15, 1991

the running buffer (7)to optimize a given separation, they do not represent general approaches. The method of choice for this seems to be modification of the inner surface of the capillary through chemical derivatization. However, good precision and reproducibility as well as successful intercapillary comparison hinge critically upon the reliable manufacture of capillary coatings with adequate chemical and temporal stability. Derivatization sometimes also leads to retention of the analytes, further complicatingthe interpretation of migration times. While it is too early to declare this insuperable, no rigorously proven method for it exists today. As a result, the search for alternative solutions to deal with variations in lc remains urgent. Numerous workers have found that v, (or l/t,), as a function of E (or V), deviates positively at high values of E, an effect attributed to increase in the temperature of the running buffer as a consequence of Joule heating (8-14). More specifically, this stems from the large temperature coefficient of the 7 of water which decreases by roughly 2% /"C between 20 and 40 "C (15). On the other hand, the changes in le,la, and t as a function of T are negligibly small (11,12,16,17). The sensitive dependence of v, and, hence, t, through 9 upon temperature is a drawback to the use oft, in specifying an analyte in an electropherogram because precise control of the temperature is essential to obtaining adequate precision of t,. Although some commercial CZE instruments are equipped with temperature control through air or liquid cooling of the capillary, accurate T control of the capillary and assurance of temperature uniformity along the capillary is difficult, if not impossible, to attain for two reasons. First, the two ends of the capillary in contact with the buffer solutions and the region through the detector are not subjected to temperature control in all existing instruments. Even if the buffer solutions and the air in the oven are maintained at the same temperature, differences in their heat capacities and, thus, heatdissipating capabilities persist. Secondly, Joule heating of the buffer solution during a run, an inevitable result of passage of electrical current through the capillary, almost always gives rise to significant temperature elevations in the capillary. In fact, a temperature increase of approximately 45 "C from the ambient temperature at the start of a run to the steady-state temperature during the run under typical operating conditions (with natural air convection) has been reported (11). Examination of eq 1reveals that even the traditionally popular pep (used in specifying an analyte in electrophoresis) is afflicted with the same malady through its association with 9 in that the operating temperature needs to be specified. To this end, the generality of pepcannot be exploited in relating the results obtained with different CZE instruments as the temperature at which separation occurs can neither be precisely controlled nor accurately measured. The same is observed even with forced-air and liquid cooling (13). However, this by no means undercuts the necessity to control the temperature of the separation condition so as to avoid analyte denaturation or degradation, drastic pH changes of the medium and buffer evaporation. To the extent that accurate temperature control during separation is not always possible, it becomes necessary to explore other means of specifying an analyte in an electropherogram. Relative Migration. As defined below, the relative migration (t,/t,) affords a solution to the problem of capillary temperature changes. Inspection of eq 5 leads to the following expression for t,, the migration time of a reference standard

t, =

4 r

1

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bination of eqs 5 and 6 gives t,/t,:

(7) Expression 7 is valid under the condition where the average temperatures during the periods from the start of a run to t, and t , are identical. This condition is satisfied if t, and t, are large compared to the time required for thermal equilibrium to be established soon after the commencement of a run and if no significant drift in the capillary temperature occufs during separation. Examination of eq 7 reveals no term that is temperature-dependent, given the fact that lC,l,, {, and f(Ka) are all relatively temperature-insensitive (11,12,16, 17). Thus, tm/t,is immune to the adverse effects associated with capillary heating. Nevertheless, a reference standard is mandatory for the utility of tm/t,. This is problematic, particularly in the analysis of complex mixtures where selecting a well-behaved reference standard (except for neutral species) with an appropriate migration time in the electropherogram can be arduous. Besides, difficulty arises from samples containing analytes with widely different migration times, which leaves t m /t, vulnerable to thermal drift. tm/t, is also incompatible with step or gradient potential runs. Furthermore, successful intercapillary data comparisons require that the { i s are identical and a common reference standard is agreed upon by the practitioners. AU the restrictions discussed above drastically limit the practical use of t,/t, in routine analyses. Migration Index. Plots of v, (or l / t m ) against, I, the current, consist of straight lines even at the high values of I typical in ordinary CZE applications with or without cooling (8-13). In fact, the relationship between E and I has been used as a test of T control (11, 18). To account for this, Hjert6n (16) and Tsuda (19) had derived the following expression to relate v, and i, the current density:

where k is the specific conductance of the running buffer. The slope of the plot of v, against i contains 9 and k, both exhibiting rather sensitive temperature dependencies. But 9 and k change in such a way that k7 remains constant for small variations in temperature (20). In fact, the product of the limiting molar conductivity of an electrolyte (A") and the viscosity coefficient of the solvent (7") is known as the Walden product whereas the assertion that Aoqo is inqlependent of temperature is termed the Walden rule (21,22). The condition of the Walden product as well as the validity of the Walden rule have profound influences on the index and will be discussed later. The easily measured I can be used to monitor v, and, therefore, correct for any effect that temperature has on .,v This is accomplished by integrating i / L against time which results in a migration index (MI) as defined below:

MI =

Atmi dt

(9)

It can be shown that MI can be expressed as follows (see Appendix A):

(6)

where {, is the { potential of the reference standard. Com-

MI is a function of

lC and la. This renders

MI useful in

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specifying analytes separated in a given buffer using capillaries with identical CC's. MI is, in fact, the slope of the plot of i against Y , which, as discussed earlier, is insensitive to temperature. As a result, MI should show superior performances compared to t, in terms of precision, reproducibility, and interlaboratory data transferability. In addition, MI is independent of the potential (or electric field) utilized in the separation. This suggests that MI can be used to relate the results obtained in runs carried out using different constant or gradient potentials. Moreover, MI is neither a function of the length nor inner diameter (i.d.1 and the capillary. Consequently, data transfer between capillaries of distinct dimensions is straightforward. Adjusted Migration Index. Application oft, and MI is restricted to runs performed in capillaries with identical {is, as revealed in eqs 5 and 10, respectively. To ensure that different capillaries possess the same {is, meticulous control of the coating manufacturing procedures, good temporal stability of the coatings and reproducible equilibration conditions are vital. Such is difficult to accomplish and, in most instances, untenable in light of the intrinsic differences that exist even amongst capillaries manufactured by the same company from batch to batch. To exacerbate matters further, undesirable adsorption of sample constituents could alter (,, resulting in a changed pea. To allow specification of analytes without the constraints imposed by temperature- and (,-related considerations, an adjusted migration index (AMI) is proposed. Suppose (MI), denotes the MI of an unretained, neutral marker. Then AMI is defined as follows:

Substitution of eq 10 into eq 11 gives

AMI = 3kq/2c{,f(~a)

(12)

It can be seen that AMI is dependent upon (, in a given running buffer, but not lC or temperature. Thus, AMI has the capability of being used to specify analytes determined not only in capillaries of different dimensions using distinct applied potentials, but also those with different surface compositions (and, hence, {c's). This relaxes the stringent requirements placed upon the capillary coating manufacturing processes while facilitating the practical transfer of AMI data between laboratories. A problem arising from the use of MI and AMI in the transfer of data between capillaries with different i.d.'s is that the i.d.'s of the capillaries concerned have to be known with an accuracy of within 0.5%. This aspect of capillary manufacturing technology presents a problem to the performance of AMI. In addition, application of AMI in data transfer requires that the concentrations of the buffers used be controlled to the same degree of accuracy. However, the latter problem can be solved with adequate attention to details. EXPERIMENTAL SECTION Detection. The laser-induced fluorescence detector employed in this study has been described elsewhere (7). Briefly, a laser beam (350 nm) is focused on-column into the detection region located at about 15 cm from the exit end of the capillary. A microscope objective is used to collect and direct the fluorescence onto a photomultiplier tube. Scattered light is excluded from passage onto the photomultiplier tube by cutoff and spatial filters. Capillary Electrophoresis. The CZE setup has also been described (23). All the capillaries used in this study (Polymicro Technologies, Phoenix, AZ) were treated with a 50/50 (v/v) methanol/water mixture followed by 0.1 M NaOH (aq), each for 30 min. Then they were equilibrated with the running buffer for at least 12 h before use. The dimensions of the capillaries and other pertinent information specific to each study are given in

Table I. Comparison of Precision of t,, t,/t,, and MI" tlb

mean

t2b

t3b t2/tl

2.63 3.56 4.11 RSD, % 0.7 0.7 0.7

1.36 0.2

t3/tl MIIC MI2' M13C 1.57

1.38 0.05

1.87

2.16

0.05 0.05 'Conditions: V = 30.0 kV; L = 65.0 cm; i.d. = 50 pm; buffer, 10 mM sodium phosphate; pH 6.62;T,capillary cooled by ambient air (22 "C). Procedure: Successive injections were made between 1 and 2 min after the completion of each previous run. Notation: ti and MIj denote the t , and MI of analyte j , respectively, while the degrees of freedom (n - 1) were 10. *In minutes. 'In Coulombs per cubic centimeter. 0.2

the Results and Discussion. All injections were by electromigration at 30 kV for 1s. All the chemicals used in preparing the running buffers are reagent grade, and the water is conductivity grade. The analytes in the sample buffer are (1) coumarin 2 (7hydroxy-4-methylcoumarin), (2) coumarin 343 (syn: 1,2,4,5,3H,6H,10H-tetrahydrobenzopyrano(9,9a,l-gh)quino~~10-one-9-carboxylicacid), and (3)disodium fluorescein (Eastman Kodak, Rochester, NY)each present at 1 X lo4 M and dissolved

in the running buffer. Data Acquisition. A DT2827 A/D converter (Data Translation, Marlboro, MA) was configured in the two-channel collection mode to simultaneously acquire signals from two multimeters (Keithley,Cleveland, OH) with the data stored in an IBM PC/AT microcomputer (Boca Raton, FL). The Model 160B multimeter was used to monitor the current from the photomultiplier tube to record the electropherogramswhereas the Model 197 multimeter records the electrophoretic current. A total of 3000 data points were collected from each channel while ensuring that at least 1500 points were acquired before the appearance of the fastest migrating analyte peak. Data Processing. After the completion of each run,the data were processed with a BASICprogram capable of first identifying the migration time of each analyte by the location of the maximum height of its peak and then calculating MI through numerically integrating the current with time. Depending on the study, the program also evaluated the AMI, t,/t,, pep,Et,, and Et,/L of each analyte. RESULTS AND DISCUSSION Precision of Migration Data. The importance of precision of migration data to a separation technique needs no further elaboration. It is, therefore, of interest to compare the performances of t,, t,/t,, and MI in this regard. As depicted in Table I, the precision of each of the parameters, as indicated by the RSDs, is impressive. However, the precision of MI and t,/t, is clearly superior to that of t,. This lends support to the contention that thermal effects figure prominently in the variations oft, in the present set of experimental conditions, which is quite typical for a homemade system with natural air convection cooling. As mentioned before, both t,/t, and MI are rather temperature-insensitive, in contrast to t,. The RSDs for MI are four times smaller than those for t,/t,. An explanation for this might be the vulnerability of t,/t, to thermal drift on the time scale of the tm's of the analytes. In the case of MI, since I is measured throughout the run time, the Y , of the analyte is known a t any instant and, as a result, any changes in Y, due to thermal effects are corrected for in the evaluation of MI. This accounts for the slightly better precision of MI than of t,/t,. Relating Results Obtained in Constant-Potential Runs. In CZE method development, other than varying the pH, buffer type and ionic strength, the most common parameter to manipulate is the E employed. Whereas separation efficiency a t low E's is limited by molecular diffusional spreading of the analyte zone, high E's cause thermal band broadening (1). A compromise between these two extremes needs to be struck to minimize the separation time while allowing adequate resolution of the components of interest. Besides, it is advantageous to be able to make use of CZE data

ANALYTICAL CHEMISTRY, VOL. 63, NO. 24, DECEMBER 15, 1991

Table 11. Comparison of Parameters in Constant- and Programmed-Potential Runsa E, V cm-l

tl b t2b t3b 103~tic io3~t2c 103Et3' r2d r3d t2/tl t3/tl

MI1' MI2' MI3'

154

307

462

3.5 min 307-462

8.40 11.41 13.08 1.29 1.75 2.01 -10.2 -13.8 1.36 1.56 1.38 1.88 2.15

4.31 5.85 6.73 1.31 1.80 2.07 -10.4 -14.0 1.36 1.56 1.38 1.87 2.15

2.48 3.36 3.88 2.01 2.07 1.79 -11.4 -15.8 1.36 1.57 1.37 1.85 2.14

3.94 4.80 5.30 1.29r 1.68' 1.91f -9.38 -12.99 1.22 1.35 1.38 1.87 2.15

"Conditions: as in Table I except for the V used. Procedure: The value of each parameter was computed from the mean of the data from two separate but consecutive runs with the second injection made within 2 min of the completion of the first run. * In minutes. In volt minutes per centimeter. In cubic centimeters per kilovolt per minute. 'In Coulombs per cubic centimeter. 'Calculated from t,(307 V cm-') + ( t , - tJ(462 V cm-') where t , = 3.50 min. BCalculated from L(l/[t,(307 V cm-') + ( t j - tJ(462 V cm-')I

- l/[t.(307 V cm-') + ( t l - t.)(462 V cm-')]}.

obtained using a different E in the literature or in the same laboratory at an earlier time. Hence, it would prove to save both time and effort if the parameter which specifies an analyte in the electropherogram is independent of the applied

E. An obvious candidate for this is pep. However, due to the fact that different amounts of power are generated in the capillary at different E's, the average temperature of the buffer solution within the capillary differs from one E to another. As shown in refs. 18 and 24, the temperature rise within the capillary is roughly proportional to E2. This results in large changes in pepthrough its dependence upon 7 (eq l),which renders the assignment of previously identified analytes to peaks obtained using a different E a separate effort. With analyte 1 indicating vW, it can be seen in Table I1 that the magnitude of pepincreases as E increases and the changes in the pep(s of analytes 2 and 3 obtained at 154 vs 462 V cm-l exceed 11%. Even though attempts have been made in minimizing temperature elevation in the capillary through air (18, 25-27) and liquid cooling (13, 27) in typical running conditions, significant decreases in 7 persist at high E's. It has been demonstrated that a Peltier thermoelectric device can effectively control capillary temperature (18),but it is not conveniently accessible. Therefore, it is not fruitful to utilize pepto relate results from runs performed at different E's. By the same token, multiplying t, by E does not rid the resulting parameter of its dependence upon 7,and thus, T, as revealed in Table I1 and eq 5. t,/t,, MI, pep,t,, and Et, at various E's are compared in Table 11. As expected on the basis of eq 5, the tm'svary widely as a function of E. The pep'sand Et,'s exhibit the same behavior except that the variations are somewhat smaller than those for the t,'s. This can be explained by the fact that the dependence of pepand Et, on E is, unlike t,, not explicit but manifests itself through 7. On the other hand, both t,/t, and MI remain quite constant as E is changed. Thus, it can be concluded that t,/t, and MI are virtually independent of the E used in the separation. Hence, t,/t, and MI can conveniently be utilized in the comparison of data obtained in separations carried out with distinct E's. Relating Results Obtained in Gradient-PotentialRuns. Although disparate in principles of operation, GC, HPLC, and

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CZE all share a common attribute, namely the capability of rapidly resolving a mixture of analytes with widely different physical properties through the temporal adjustment of a parameter in the separation condition. In GC and HPLC, the most popular choices are temperature and eluent programming to allow adequate resolution of analytes possessing, respectively, a wide range of volatilities and hydrophobicities in a reasonably short period of time. The demand for this in CZE is no less rigorous, since samples might consist of analytes with opposite polarities and very different electrophoretic mobilities. Depending on the application, one way of shortening the separation time of analytes having a wide range of pK values is the employment of a dynamic pH gradient (28,29). An equally promising approach involves the use of a potential gradient (14). The upper limit of the E utilized in a constant-potential separation is determined by the pair of analytes that are most difficult to resolve. Hence, the potential can be stepped up immediatelysubsequent to the elution of the two components corresponding to the potential-limiting pair of analytes. The potential to step up to is, in turn, decided by the next pair of analytes that are hardest to resolve but yet to emerge. Likewise, the potential can be manipulated in a similar fashion to minimize the separation time while optimizing the resolutions of all the remaining components. Of course, care must be taken not to exceed the critical point where thermal convection becomes intolerable. In the implementation of such a strategy, one is faced with the task of assigning each analyte to a different migration time or relative migration once a new potential program is attemped. This renders the process both cumbersome and time-consuming. However, the use of MI bypasses such difficulties since the Y,'S of all the analytes are monitored continuously through I throughout the run time. Thus, any change in v, due to the application of a changing potential is corrected for in MI. The behaviors oft,, t,/t,, and MI at constant and gradient potentials are documented in Table I1 where the last column depicts the results obtained in a programmed-potentialrun with an abrupt increase in V from 20.0 to 30.0 kV at 3.50 min into the separation. As expected, t , varies widely in the constant- and programmed-potentialruns whereas t,/ t, remains unchanged at different constant potentials, but decreased in the programmed-potentialrun. The behavior of tm/t,can be attributed to the fact that eq 7 is derived on the assumption that E is invariant with time. This is valid for constant-potential runs, but not programmedpotential runs. Simply correcting t,, t,/t,, and pepwith the temporal function of E still fails to relate the tm's, tm/t;s, and pep's in constant- and programmed-potential runs as the change in the temperature-dependent 7 at different E's is left unaccounted for, as shown in Table 11. MI, however, is not only unaltered in the programmed-potentialrun, but its value is the same as in the corresponding constant-potential runs. Consequently, MI can be used to relate the results obtained in different constant- and gradient-potential runs. Relating Results Obtained in Capillaries of Different Lengths. In GC and HPLC, it is possible to relate the results obtained in columns of different lengths by simple geometric corrections, provided that the capacity factors of the analytes can be reproduced from column to column. Extension of the previous statement to CZE is valid if (p, + p?p)can be made constant from capillary to capillary. In practice, the transfer of data between capillaries of different lengths in CZE is, however, not so straightforward. This is largely a consequence of the inevitable temperature differences of the buffer solutions during separation because of the distinct extents of Joule heating and varied heat-dissipating capabilities of the capillaries with different lengths when a constant V is employed.

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Table 111. Comparison oft,, t , E / L , t , / t , , and MI Obtained in Capillaries of Different Lengths’

Table IV. Comparison of t,, t,/t,, MI, and AMI Obtained in Capillaries with Different I;’s

L, cm tlb t2b t3* 10-2Etl/Lc 10-2Et2/Lc 10-2Et3/ L‘ t2/tl t3/tl MIld M12d M13d

55.0

65.0

75.0

1.71 2.35 2.72 2.33 3.20 3.71 1.37 1.59 1.31 1.80 2.08

2.69 3.68 4.25 2.48 3.40 3.93 1.37 1.58 1.32 1.80 2.08

3.88 5.36 6.19 2.59 3.93 4.13 1.38 1.60 1.32 1.81 2.08

‘conditions: as in Table I except pH 6.75. Procedure: as in Table 11. In minutes. In kilovolt minutes per square centimeter. Coulombs per cubic centimeter. The resulting temperature differences render (pm + pep) different in capillaries with different lengths through 7 (eqs 1 and 3). As shown in refs 18 and 24, the temperature rise of the buffer solution within the capillary from the start of a run to the steady state is roughly proportional to 1/L2. Hence, even if the effects of the distinct E’s together with the L’s are taken into account, the transfer of results between capillaries with different lengths remains untenable in the case where the capillary is cooled by natural air convection. A substantiation of this is revealed in Table I11 where the Et,/L’s obtained in capillaries with three different lengths for all the analytes vary as the capillary length changes. While one could make the argument of performing separations in capillaries of different lengths with identical E’s, such an approach is cumbersome in practice and inaccurate in light of the approximate nature of the proportionality of T increase and (E/LI2. Nonetheless, the transfer of results between capillaries of different lengths remains useful not only in intercapillary data comparison, but would also save time in method development. Recall that in eq 5, t, is directly proportional to L and E is inversely proportional to L for constant V operation. Provided that secondary thermal effects are not serious, one could always shorten the analysis time by using a shorter capillary. As mentioned earlier, t m / t ,and MI are insensitive to effects associated with T changes. Thus, the differences in the 7”s of the buffer solution in capillaries with different lengths during separation would not affect either parameter. Indeed, the results shown in Table I11 are in agreement with expectation in that both the t,/t,’s and MI’s of the three analytes did not display any significant change in the three capillary lengths studied. Consequently, both t,/t, and MI can be used to relate the results obtained in capillaries of different lengths. Moreover, the fact that the MI’s stayed constant from one length to another gives an indication of the high degree of uniformity of fc throughout the length of the capillary. Since nonuniform lc values within the capillary result in viscous flow and, therefore, loss of efficiency (30),the constancy of t,/t, and MI as a function of L can be utilized as a means of determining whether nonuniformity in the CC of the capillary (which could be a consequence of intrinsic differences in the physical properties of the wall materials or severe solute adsorption) exists. Relating Results Obtained in Capillaries with Different le's. The wide variety of coating materials from different commercial sources only adds to the difficulty in the transfer of CZE data obtained in different capillaries. Even if the capillaries in use possess coatings comprising the same materials nominally, it is unlikely that the requirement of

t1b t2b t3* t2/tl t3/tl MIlc M12c MI3‘ AMI2‘ AM13C

capillary A

capillary B

3.46 4.90 5.76 1.41 1.37 1.41 1.99 2.34 -4.85 -3.57

3.13 4.28 4.93 1.66 1.58 1.30 1.78 2.05 -4.81 -3.55

Conditions: as in Table I11 with L = 75.0 cm. Procedure: capillary A, as in Table 11; capillary B, Capillary A was flushed with 0.1 M NaOH(aq) for 6 h followed by equilibration with the running buffer for 12 hrs and the subsequent procedure was identical minutes. ‘In Coulombs per cubic to that for Capillary A. centimeter. identical {,’s can be fulfilled with the most time-consuming and involved capillary pretreatment procedures. The utility of AMI rids the analyst of such concerns as AMI is not only unaffected by T, but it is also independent of the fC of the capillary. However, since resolution is dependent upon pm ( I ) and, hence, {,, care must be exercised to ensure that adequate resolution is preserved in separations performed in capillaries with different s:{. A major area of CZE involves suppressing v, by making negligible. In that case, MI would be adequate for intercapillary data transfer. A comparison oft,, t,/t,, MI, and AMI obtained in two capillaries with different { i s is shown in Table IV. Since the capillaries are of identical dimensions and the same E is used in the separations, the difference in thes:{ is reflected in the distinct tm’s of each analyte in the two capillaries. As expect4 on the basis of eqs 7 and 10, respectively, both the t,/t,’s and MI’s changed from one capillary to another. Of all the parameters outlined, only AMI remained relatively unaltered. In fact, the AMI’S for each analyte differed from each other by less than 1% between the two capillaries. This demonstrates the feasibility of utilizing AMI in relating the results obtained in capillaries with different {s:. Accordingly, no theoretical barrier obstructs the use of AMI in the transfer of data obtained in capillaries composed of different materials (e.g. Teflon, Pyrex, etc.). Relating Results Obtained in Capillaries with Different i.d.’s. Disputes over the optimal capillary i.d. in CZE analyses are many-faceted and depend upon the relative degree of separation efficiency and detection sensitivity demanded by the task at hand. Use of a large-i.d. capillary (e.g. 200 pm) maximizes the concentration detection sensitivity with the popular UV absorption detector while sacrificing some useful separation efficiency through severe thermal band broadening. On the other hand, concentration detection sensitivity becomes a matter of concern despite a gain in separation efficiency when a small i.d. capillary (e.g. 5 pm) is utilized. In fact, due to the mutual exclusiveness of detection sensitivity and separation efficiency, any efforts in pushing toward a standardized capillary i.d. are bound to be unsuccessful. Therefore the advantages realized over the ability of relating the results obtained in capillaries with different i.d.’s remain attractive. In a previous section, it has been demonstrated that one could use MI as a parameter in relating the results obtained in capillaries of different lengths. This is possible because of the T-insensitive nature of MI. However, MI is not only a function of Ca, but also lC. While it is possible to study the behavior of MI with the assurance of constancy in tCby simply cutting off parts of the same capillary, the same is not ap-

rC

ANALYTICAL CHEMISTRY, VOL. 63, NO. 24, DECEMBER 15, 1991

Table V. Comparison of t,, t,/t,, MI,and AMI Obtained in Capillaries with Different I.d.'s id.. um t1 b t2b t 3b t2/tl t3/tl MIIC MI2' MI3' AM12c AM13c

20

50

3.47 4.67 5.33 1.35 1.53 1.25 1.70 1.93 -4.86 -3.60

3.36 4.68 5.43 1.39 1.62 1.40 1.95 2.26 -4.96 -3.66

nConditions: as in Table IV except V = 25.0 kV and pH 6.66. Procedure: as in Table 11. minutes. 'In Coulombs per cubic centimeter. plicable to i.d. studies in that no readily accessible means exists that would ensure that the { i s of capillaries with different i.d.'s are identical. One method which permits the determination of lcin a manner free of constraints imposed by T effects involves the measurement of the streaming potential (31),but it necessitates the construction of specialized instruments and is, therefore, not conveniently accessible. As a result, no deliberate effort was made here to guarantee that the capillaries possess identical {is. In the present study, even with meticulous attention devoted to ensuring that the capillaries studied were pretreated identically, the resulting le's still differed somewhat, as unveiled in the values of MI1 in Table V. For the same reason, the MI'S of each of the remaining analytes differed from one capillary to another. Surprisingly, t, displayed smaller changes from one i.d. to another in Table V, an observation contrary to many previous studies carried out in our laboratory (data not shown). As a matter of fact, t , is usually observed to increase by as much as 30% from a 50-pm4.d. capillary to a 20-pm one because of the poor heat-dissipating capability of the former and is assumed to be unsuitable as a parameter for the transfer of data between capillaries with different i.d.'s. In the present study, the effect of the smaller t) of the buffer solution in the 50-pm-i.d. capillary compared to that in the 20-pm one is accidentally offset by the smaller lCof the former compared to that in the latter, thereby concealing the sensitive dependence of t , upon T. The coincidental nature of the invariant tm's from one i.d. to another is further supported by the clear trend of a positive rate of increase of the tm's in the 50- over the 20-Fm capillary from analytes 1 to 3. As revealed in eq 5, had t) remained constant from one i.d. to another, no such increase should have been observed. Another manifestation of the smaller in the 50-pm-i.d. capillary compared to that in the 20-pm one can be found in the greater t,/t, in the 50-pm compared to 20-pm capillary for each analyte (eq 7). The use of tm/t, in relating the results obtained in capillaries with different i.d.'s is, as discussed earlier, unsatisfactory due to its dependence upon fC, which leaves AMI the only feasible alternative. Despite its insensitivity to T and lC,the accuracy of AMI in the transfer of data between capillaries with different i.d.'s is limited by the accuracy with which the i.d.'s of the capillary can be determined. Recall that i is computed from I and A , the cross-sectional area of the inner space of the capillary. Since an error of h470 in the i.d. of an averaged-sized capillary (50 pm) is not uncommon (32),the small difference between the AMI'S from one i.d. to another in the present study (